Question

Which of the following parameters are the same for all hydrogen-like atoms and ions in their ground states?

• A. Radius of the orbit
• B. Speed of the electron
• C. Energy of the atom
• D. Orbital angular momentum of the electron

Answer 1

Answer: (D)

Orbital angular momentum of the electron

According to Bohr's model of an atom, energy of nth orbit is given by: $E_n=-13.6\frac{Z^2}{n^2}eV$

Radius of nth orbit, $r_n=0.529\frac{n^2}{Z}{A}^o$

Speed of an electron in nth orbit, $v_n=2.18\times {10}^6\frac{Z}{n}m/s$

And orbital angular momentum, $L_n=\frac{nh}{2\pi }$

$⟹$ Radius of the orbit, speed of the electron, and energy of an atom depends on $Z$ whereas orbital angular momentum is independent of $Z$.

Hence, orbital angular momentum remains the same for all hydrogen like atoms and ions in ground state $(n=1)$.